### Question 5

SSC-CGL 2019 June 13 Shift 1

If 2 sinθ = 5 cosθ, then (sinθ + cosθ)/(sinθ - cosθ) = ?

- 5/3
- 9/5
- 2/3
- 7/3

### Solution in Short

2 sinθ = 5 cosθ gives tanθ = 5/2. To find (sinθ + cosθ)/(sinθ - cosθ) divide numerator and denominator by cosθ to get (tanθ + 1)/(tanθ - 1) = (5/2 + 1)/(5/2 - 1) = 7/3 answer!

### Solution in Detail

Given $\displaystyle 2\sin \theta = 5 \cos \theta$

$\displaystyle \implies \frac{\sin \theta}{\cos \theta} = \frac 52\text{ . . . (1)}$

Remember componendo dividendo?

If $\displaystyle \frac xy = \frac pq \implies \frac{x + y}{x - y} = \frac{p + q}{p - q}$

$\displaystyle \therefore \text{ from (1) } \frac{\sin \theta + \cos \theta}{\sin \theta - \cos \theta} = \frac{5 + 2}{5 - 2}$

$\displaystyle \implies \frac 73 \:\underline{Ans}$

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